Question

What is the current around the nucleus due to the motion of the electron?

Answer 1

For Hydrogen;




\[m_e =9.1\times10^{-31} [\text{kg}]\\q_e=1.6\times10^{-19} [\text C]\\R =5\times10^{-11} [\text m] \]

Answer 2

\[A =\pi R^2=8\times10^{-21} [\text m^2]\]

Answer 3

\[F_\text{electric} =F_\text{centripetal} \\
\frac{e^2}{4\pi\varepsilon_0 R^2}=\frac{mv^2}R \\
v=\sqrt\frac{e^2}{4\pi\varepsilon_0 Rm}
=2.3\times10^6[\text m/\text s]\]

Answer 4

\[T=\frac Cv=\frac{2\pi R}v=1.4\times10^{-16}[\text s]\]

Answer 5

\[I=\frac qT=\frac{q_e}T=\frac{1.6\times10^{-19} [\text C]}{1.4\times10^{-16}[\text s]}\approx1[\text {mA}]\]

Answer 6

\[\large\color{red}{\cancel {\color{black}{q_e}}}\quad\color{red}{e=-q_e}\]